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Proceedings of HTC2003 

2003 ASME Heat Transfer Conference 
July 21-23, 2003, LasVegas, Nevada USA 



HT2003-47406 



TRANSMITTANCE AND RADIANCE COMPUTATIONS FOR ROCKET ENGINE 

PLUME ENVIRONMENTS 



Gopal D. Tejwani 

Lockheed Martin Space Operations 

Systems Engineering and Advanced Teclnnologies Department 

Jolin C. Stennis Space Center 

Stennis Space Center, Mississippi 39529 

e-mail: gtejwani@ssc.nasa.gov 



ABSTRACT 

Rocket engine exhaust plume is generally thermal in char- 
acter arising from changes in the internal energy of constituent 
molecules. Radiation from the plume is attenuated in its passage 
through the atmosphere. In the visible and the infrared region 
of the spectrum for clear-sky conditions, this is caused mainly 
through absorption by atmospheric molecular species. The most 
important combustion-product molecules giving rise to emission 
in the IR are water vapor, carbon dioxide, and carbon monoxide. 
In addition, the high temperature plume reacting with the sur- 
rounding atmosphere may produce nitrogen oxides, in the bound- 
ary layer, all of which are strongly emitting molecules. Important 
absorbing species in the atmosphere in the engine plume envi- 
ronment are H2O, CO, CO2, CH4, N2O, NO, and NO 2. Under 
normal atmospheric conditions, the concentrations of O3, SO2, 
and NH3 are too small to produce any significant absorption. 
Essentially the problem comprises of the propagation of radia- 
tion from a hot gas source through a long cool absorbing atmo- 
sphere thus combining aspects of atmospheric and combustion 
gas methods. Since many of the same molecular species are re- 
sponsible for both emission and absorption, the high degree of 
line position correlation between the emission and absorption 
spectra precludes the decoupling of the optical path into isolated 
emitter and absorber regions and multiplying the source band 
radiance by the absorber band transmittance in order to arrive 
at the transmitted radiance spectrum. Also, very strong thermal 
gradients may be encountered. All this suggests that a layer- 
by-layer computation is called for. The pathlength through the 



plume and the atmosphere is assumed to go through a certain 
number of layers, each of which is considered to have all molec- 
ular species in local thermodynamic equilibrium at constant tem- 
perature and pressure within the layer. Radiative transfer prob- 
lems can be visualized as a set of parallel layers orthogonal to 
the line of sight, each with an input radiance from the previ- 
ous layer and an output radiance to the subsequent layer. The 
MODTRAN (MODerate resolution TRANsmission) code is ide- 
ally suited for layer-by-layer absorption/emission calculations 
for atmospheric molecular species. We have utilized MODTRAN 
4.0 computer code, implemented on a Power Mac G3, for the 
radiance and transmittance computations. The MODTRAN code 
has been adapted for the engine plume radiance computations. If 
the plume composition and flowfield parameters such as the tem- 
perature and pressure values are known along the line of sight by 
means of the experimental measurements or (more likely) CFD 
simulations, one can compute the radiance from any plume with 
high degree of accuracy at any desired point in space. Emis- 
sion and absorption characteristics of several atmospheric and 
combustion species have been studied and presented in this pa- 
per with reference to the rocket engine plume environments at 
the Stennis Space Center. In general transmittance losses can 
not be neglected for any pathlength of 2 m or more. We have 
also studied the effect of clouds, rain, and fog on the plume ra- 
diance/transmittance. The transmittance losses are severe if any 
of these occur along the line of sight. Preliminary results for the 
radiance from the exhaust plume of the space shuttle main engine 
are shown and discussed. 



Copyright © 2003 by ASME 



Keywords: Transmittance, Plume Radiance, MODTRAN, 
Rocket Engine Plume 



NOMENCLATURE 

Ay monochromatic absorption 
E" energy of the lower state 
rotational partition function 
vibrational partition function 
line intensity per absorbing molecule 
temperature, K 

spectral absorption coefficient 
absorbing material amount 
line half-width at half-maximum 
differential increase in pathlength 
H wavelength 
V frequency 
Vo resonant frequency 



Qr 

s 

T 

k 



8L 



INTRODUCTION 

John C. Stennis Space Center (SSC) is NASA's desig- 
nated Center of Excellence for large rocket propulsion testing. 
Radiant-energy transfer is of fundamental importance in the un- 
derstanding and in the solution of many engineering problems in 
the SSC's rocket engine testing environments. Examples of in- 
teresting practical applications are theoretical calculations of ra- 
diant heat transfer for plume-induced environments, plume tem- 
perature measurements, and spectroscopic analysis of multi com- 
ponent gas mixtures for the engine health monitoring and for the 
EPA compliance. Rocket exhaust plume is generally thermal in 
character, arising from changes in the internal energy of con- 
stituent molecules. Radiation from the plume is attenuated in its 
passage through the atmosphere. In the visible and the infrared 
region of the spectrum for clear-sky conditions, this is caused 
mainly through absorption by atmospheric molecular species. 

Rocket engines are tested at SSC for improvement, develop- 
ment and flight certification. Although, the Space Shuttle Main 
Engine (SSME) is the most famous of rocket engines currently 
being tested at SSC, several types of hydrocarbon fuel rocket en- 
gines have also been or currently being tested at SSC. High tem- 
perature exhaust plume is responsible for very strong IR emis- 
sions due to combustion-product molecules, water vapor, carbon 
dioxide, and carbon monoxide. In addition, the high tempera- 
ture plume reacting with the surrounding atmosphere may pro- 
duce nitrogen oxides, in the boundary layer, all of which are 
strongly emitting molecules. Important absorbing species in the 
atmosphere in the engine plume environment are H2O, CO, CO2, 
CH4, N2O, NO, and NO2. Under normal atmospheric conditions, 
the concentrations of O3, SO2, and NH3 are too small to produce 
any significant absorption. Essentially the problem comprises 



of the propagation of radiation from a hot gas source through a 
long cool absorbing atmosphere thus combining aspects of at- 
mospheric and combustion gas methods. Since many of the 
same molecular species are responsible for both emission and 
absorption, the high degree of line position correlation between 
the emission and absorption spectra precludes the decoupling of 
the optical path into isolated emitter and absorber regions and 
multiplying the source band radiance by the absorber band trans- 
mittance in order to arrive at the transmitted radiance spectrum. 
Also, very strong thermal gradients may be encountered. All 
this suggests that a layer-by-layer computation is called for. The 
pathlength through the plume and the atmosphere is assumed to 
go through a certain number of layers, each of which is consid- 
ered to have all molecular species in local thermodynamic equi- 
librium at constant temperature and pressure within the layer. 
Radiative transfer problems can be visualized as a set of parallel 
layers orthogonal to the line of sight, each with an input radiance 
from the previous layer and an output radiance to the subsequent 
layer The MODTRAN (MODerate resolution TRANsmission) 
code is ideally suited for layer-by-layer absorption/emission cal- 
culations for atmospheric molecular species. We have utilized 
MODTRAN 4.0 computer code, implemented on a Power Mac 
G3, for the radiance and transmittance computations. A brief de- 
scription of the main features of the code is given in the next Sec- 
tion followed by some theoretical background. Transmittance 
computations and results are discussed. The MODTRAN code 
has been adapted for the engine plume radiance computations. 
The SSME radiance computations and results are shown. For 
both transmittance as well as radiance computations, parametric 
studies with respect to the concentration of the relevant molecu- 
lar species and the pathlength have been performed. 



MODTRAN PROGRAM 

MODTRAN is a moderate resolution model and computer 
code for predicting atmospheric transmittance and background 
radiance in the microwave, infrared, visible and near ultraviolet 
spectral regions for any given atmospheric path. This code has 
evolved from the LOWTRAN (LOW resolution TRANsmission) 
codes, with LOWTRAN 7 being the last and the most current 
version [1]. Its spectral resolution is 20 cm~' Full Width/Half 
Maximum (FWHM) with calculations being done in 5 cm~' in- 
crements. MODTRAN increases LOWTRAN's spectral reso- 
lution from 20 to 2 cm~' (FWHM). It models molecular ab- 
sorption of twelve atmospheric species as a function of tem- 
perature and pressure. Molecular absorption is calculated in 1 
cm~' spectral bins. The MODTRAN band model uses three 
temperature-dependent parameters, an absorption coefficient, a 
line density parameter and an average linewidth. The twelve 
molecular species are water vapor, carbon dioxide, ozone, ni- 
trous oxide, carbon monoxide, methane, oxygen, nitric oxide, 
sulfur dioxide, nitrogen dioxide, ammonia and nitric acid. Their 



Copyright © 2003 by ASME 



absorption properties (the band model parameters) are calculated 
from the HITRAN line atlas [2], which contains all lines in the 
- 17,900 cm~' spectral region that have significant absorption 
for atmospheric paths. Further details of the code are available in 
Ref. [3]. We have implemented MODTRAN 4.0 computer code 
on a Power Mac G3. 

THEORETICAL BACKGROUND 

The theoretical foundations for the radiance and the atmo- 
spheric transmittance computations are available in two pioneer- 
ing books by Penner [4] and Goody [5]. The main equation of ra- 
diative transfer, although complex, can be summarized in a single 
integro-differential equation in terms of physical parameters per- 
tinent to the particular problem of radiative transfer For the at- 
mosphere, these parameters are represented by factors like mete- 
orological quantities, atmospheric constituents, specific sources 
of radiation within or external to the atmosphere, geometrical 
configurations of sources, and the detectors of radiation. Taking 
into account all these factors and assuming that the earth's at- 
mosphere can be considered as made up of plane layers parallel 
to an essentially plane earth surface, a complete set of equations 
is available in Ref. [5] for different approaches or methods of 
calculating atmospheric transmittance and radiance. The most 
accurate method is line-by-line calculation. It is based on a set 
of line spectral parameters that describe the molecular lines in 
which radiation is absorbed or emitted. However, even for a nar- 
row spectral range, thousands of molecular lines need to be con- 
sidered. Therefore, routine transmittance computations are not 
feasible to be carried out by utilizing the line-by-line approach. 
The preferred methodology for these computations is based on 
band-models [5] at tremendous reduction in computational re- 
sources without too much sacrifice in accuracy. LOWTRAN and 
MODTRAN computer codes utilize band model approach. Ear- 
lier versions of the LOWTRAN computer code manuals [6] give 
detailed equations for the radiance and the transmittance calcu- 
lations using band model methodology. These equations will not 
be repeated here as the complete set of equations is very exten- 
sive. However, it would be instructive to describe the absorption 
process for a single molecular transition or line. The four essen- 
tial line parameters for each line are the resonant frequency, v„, 
the intensity per absorbing molecule, S, the Lorentz line width 
parameter, Yo, and the energy of the lower state, E" . The spectral 
absorption coefficient for the Lorentz line shape is: 



k{v) = 



Sjo 



n{v-Vo) +yl 



'=jm 



dv 



(1) 



(2) 



The line half- width at half-maximum, Y„, is by definition 
proportional to the pressure, p, and its temperature dependence 
can be computed for each transition of every molecular specie 
[7]. The line intensity is temperature dependent through the 
Boltzmann factor and the partition function as indicated in Eq. 
(3), 



S{T) 



S{Ts)QATs)Qr{T s) 

QAT)Qr{T) 



-exp 



\A39E"{T-T,) 



TZ 



(3) 



where Qv and Qr are the vibrational and rotational partition func- 
tions. Ts is standard atmospheric temperature, taken to be 296 K 
in all spectral line parameter compilations. For a homogeneous 
path, the monochromatic absorption at a frequency v is obtained 
from 



Av = 1 — Tv = 1 — exp (— fcym) 



(4) 



where Ty is the monochromatic transmission and m is the amount 
of absorbing material. 

As mentioned earlier, the MODTRAN computer code uti- 
lizes the complete band model parameters for H2O, CO2, O3, 
N2O, CO, CH4, O2, NO, SO2, NO2, NH3, and HNO3. In ad- 
dition, heavy species, which include nine chlorofluorocarbons 
(CFC's) plus C£0N02, HNO4, C«4, and N2O5 have been added 
recently. However, the band model parameters for heavy species 
are not as accurate, extensive, or complete as the twelve main 
constituents. 

MODTRAN code has the feature of utilizing one of the six 
geographical - seasonal model atmospheres or it can read user- 
defined meteorological or radiosonde data. The model atmo- 
spheres correspond to the 1962 U.S. Standard atmosphere, and 
the five supplementary models: that is. Tropical (15° N), Mid 
latitude Summer (45° N, July), Mid latitude Winter (45° N, Jan- 
uary), Subarctic Summer (60° N, July), and Subarctic Winter 
(60° N, January). Obviously, none of these models are going 
to provide a very good representation of the atmospheric condi- 
tions at the SSC. However, since we aim to do a parametric study 
of the transmittance and radiance with respect to the species con- 
centrations and since we are mostly interested in relatively small 
pathlengths (100 m maximum). Mid latitude Summer model will 
provide more than adequate starting point for this study. Com- 
plete details of the input files including the model atmospheres 
are available in Ref. [3]. 



TRANSMITTANCE COMPUTATIONS AND RESULTS 

Transmittance computations have been performed for the 
spectral range of 0.4 to 20.0 fj. This region encompasses black- 
body curves for the temperature range of interest (300 to 3200 K) 



Copyright © 2003 by ASME 



for the engine testing plume environment. As mentioned earlier, 
most of our computations have been performed by utilizing mid 
latitude summer Model. Three other Model atmospheres were 
tried, namely, U. S. Standard atmosphere, tropical, and mid lati- 
tude winter The average transmittance for 100 m pathlength was 
computed to be 0.917, 0.888, 0.928, and 0.897 forU. S. Standard 
atmosphere, tropical, mid latitude winter, mid latitude summer 
models, respectively. 

Figure la shows the total transmittance (or absorbance) 
along with absorbance due to the water vapor and water vapor 
continuum for 100 m pathlength in the spectral range of 0.4 to 
20.0 iJ. H2O has strong absorption due to two fundamental bands 
V3 and V2 centered at 2.66 and 6.27 /j, respectively. In addi- 
tion, vi fundamental (band center at 2.74 /j) and several over- 
tone and combination bands are responsible for absorption from 
0.4 to 3.5 IJ. The water vapor absorption from 10.0 to 20.0 /j 
is due to the pure rotational band [8]. For water vapor, the ab- 
sorption measured in the laboratory or in the atmosphere is usu- 
ally greater than that predicted on the basis of known positions, 
intensities and widths of the lines and previously adopted the- 
oretical line shapes. The excess absorption that represents the 
difference between the experimental and calculated values is re- 
ferred as the continuum absorption because it does not change 
rapidly with changing wavenumber. The continuum absorption 
is mostly attributed to absorption by dimers consisting of 2 bound 
H2O molecules or by clusters of several molecules. Water vapor 
continuum absorption model is based on LOWTRAN 6 [6]. CO, 
CO2 and COj absorption is shown in Fig. lb. Total transmit- 
tance is also shown for comparison. Concentration of CO2 has 
been taken to be 360 ppmv instead of using the default value of 
330 ppmv for the mixing ratio as CO2 concentration in the at- 
mosphere has been steadily increasing [3]. CO2 and CO J have 
very strong absorption bands at 4.26 and 14.98 /j corresponding 
to V3 and V2 fundamental bands, respectively, vi fundamental 
band is inactive in the infrared. The absorption at 2.69 /j is due 
to the vi H- V3 combination band. CO has a strong fundamen- 
tal band at 4.67 /j and moderately strong first overtone band at 
2.33 IJ. However, CO concentration (roughly 0.07 ppmv) in the 
normal atmosphere is too small for these and other bands of CO 
to impact the transmittance very significantly. For normal atmo- 
spheric concentrations of N2O, fundamental bands vi, V2, and 
V3 absorb noticeably at 4.50, 16.98, and 7.78 /j, respectively and 
CH4 has active and strong fundamental bands at 3.31, 3.46, and 
7.66 IJ corresponding to V3, vi, and V4 [9]. For the sake of brevity, 
N2O and CH4 absorptions are not shown here. However these 
plots are available in Ref. [10]. Contribution from other species 
such as O3, NH3, NO, NO2, and HNO3 are not shown because 
their concentration is too small in the normal atmosphere at or 
near the ground level for significant absorption to occur at rather 
small pathlength of 100 m. 

The effect of the pathlength on the total transmittance can be 
seen in Fig. 2 where the results for the pathlengths of 1, 5, and 



100 m are shown. The average transmittance for 1, 2, 5, 20, and 
100 m is 0.987, 0.981, 0.969, 0.943, and 0.897, respectively. 

We have performed parametric studies of transmittance 
vs. concentration for many species which are present in the 
plume under various engine firings. For example, CO and CO2 
in addition to H2O are the main combustion products during 
hydrocarbon-fueled rocket engine testing. Elevated levels of 
various nitrogen oxides (NO, N2O, and NO2) are generated in 
the mixing layer between the plume and the surrounding atmo- 
sphere. Parametric studies have been performed for H2O, CO2, 
CO, CH4, N2O, NO, and NO2. Any one of these strongly absorb- 
ing species affects the transmittance significantly if it is present 
in the environment at concentrations higher than 200 ppm. The 
actual transmittance computations for any given engine testing 
environment can be performed if the molecular species distribu- 
tion along the pathlength can be ascertained by CFD prediction 
or by prior on-site measurements of species concentrations from 
a previous test. Also temperature and pressure variations along 
the pathlength can be taken into account by utilizing appropriate 
layers perpendicular to the pathlength. For the sake of brevity, 
we will only show here the results for the CO2 parametric study. 
Transmittance values for 0.4 to 20 p for 360, 1000, 5000 and 
10,000ppm are shown in Fig. 3. Because of the saturation of sev- 
eral bands, the increase in absorption is less and less pronounced 
as the CO2 concentration increases. 

Scattering computations in MODTRAN are modeled same 
as in LOWTRAN 6 [6]. For the most part, under a clear sky con- 
ditions, the scattering effects are insignificant. However, under 
foggy or rainy conditions, scattering becomes the most signif- 
icant contributor to the transmission losses. This can be seen 
in Fig. 4 where the total, H2O continuum, H2O, and aerosol 
transmittance have been plotted for 0.4 to 20 /j for 5.0 mm/hr 
ground light rain. The average total transmittance for this light 
rain model is 0.063. We have also studied the effect of moder- 
ate rain rate (12.5 mm/hr) and very light rain rate or drizzle (2.0 
mm/hr). The average transmittance is 0.059 and 0.852 for the 
moderate rain model and for the ground drizzle model, respec- 
tively. 

We have considered two cases of foggy conditions: advec- 
tive fog with a visibility of 0.2 km and radiative fog with a visi- 
bility of 0.5 km. Transmission losses are much more severe for 
advective fog model because of much higher scattering effects 
from condensed water particles. Figure 5 shows the results for 
radiative fog, where the total, H2O continuum, H2O, and aerosol 
transmittance has been plotted for the spectral range of 0.4 to 
20.0 /J. The average transmittance for radiative fog is 0.409 com- 
pared to the average transmittance of 0.126 for advective fog. 



RADIANCE COMPUTATIONS AND RESULTS 

MODTRAN code is mainly designed and developed for the 
atmospheric radiance and transmittance computations. As men- 



Copyright © 2003 by ASME 



1.0-r 



0.8 ■ 



o 0.6 ■ 






0.2 ■ 



0.0 -I 



J I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I L_ 




T — I 1 1 1 1 1 1 1 1 1 f — I 1 r 



I ' ' ' I ' ' ' I 
8 10 12 

Wavelength (p) 



T 1 1 1 1 — I 1 1 — I 1 1 1 — I 1 r 



1 
14 



T 
16 



r 

18 



20 



Figure la. Total, H2O Continuum, and H2O Transmittance for 0.4 to 20 ;U for 100 m Pathlength Utilizing Mid-Latitude Summer Model Atmosphere. 
J I I I I I I I I .1 . I I I I I I I II I I I I I 1.1 I I I I I I I I ill I I 



1.0 ■ 



0.8 - 



n 0.6- 



c 

H 0.4 - 



0.2 ■ 



0.0 -I 



' ^i P \^i 



.'r 



I I J ' I I ii II 



fi 



Red ~ Total Transmittance 



Blue ~ CO2 Transmittance 
Pink ~ CO Transmittance 



1 — I — I — I — I — I — I — I — I — I — r 



— I — I — I — I — I — I — I — I — I — I — I — I — I — 
6 8 10 12 

Wavelength (p) 



T 1 1 1 1 1 1 1 1 1 1 1 1 1 T" 



1 

14 



T 
16 



18 20 



Figure lb. Total, CO2, CO J, and CO Transmittance for 0.4 to 20/7 for 100 m Pathlength Utilizing Mid-Latitude Summer Model Atmosphere. 

5 Copyright © 2003 by ASME 



H 0.4 







\ 



W'^'^^^^'^rE 



_i — I — I — I — I — I — I — I — I — I — 1_ 



VII , Ml 



Red - 100 m Pathlength 
Green — 5 m Pathlength 
Blue - 1 m Pathlength 



w> 



-p-I— I— I— p-I— I— 

8 10 

Wavelength ((i) 



', , ,, II 



Figure 2. Total Transmittance for 0.4 to 20 /j for 100, 5, and 1 m Pathfongth Utilizing Mid-Latitude Summer Model Atmosphere. 




I I I -U 




H 0.6 



H 0.4 ■ 



Red ~ 360 ppm Carbon Dioxide 
Green — 1000 ppm Carbon Dioxide 
Blue ~ 5000 ppm Carbon Dioxide 
Pink - 10000 ppm Carbon Dioxide 



if I 



I 



8 10 12 

Wavelength (|j) 



— I — I — I — I — I — I — I — I — |— 

14 16 18 



Figure 3. CO2 Transmittance for 0.4 to 20^0 for 360, 1000, 5000, and 10000 ppm Carbon Dioxide and 100 m Pathlength Utilizing Mid-Latitude Summer 
Model Atmosphere. 



Copyright © 2003 by ASME 



1.0-r 



H 0.4 ■ 



I II .' I I ', ' 



''^HT'v:: 




f/pcr^^mw^ 



]— I— I— I— p-i 1—1 |— 1 I— r 

6 8 10 12 

Wavelength (^) 




Red — Total Transmittance 
Green — Water Vapor Continuum 
Blue — Water Vapor Transmittance 
Pink - Aerosol Transmittance 



Figure 4. Total, H2O Continuum, H2O, and Aerosol Transmittance for 0.4 to 20 /7 for 5.0 mm/hr Ground Light Rain and 100 m Pathlength Utilizing 
Mid-Latitude Summer Model Atmosphere. 



1.0 



0.8- 



c 



H 0.4 ■ 




_L 



^-V\CVi 



_L 



_L 



Red — Total Transmittance 
Green -- Water Vapor Continuum 
Blue — Water Vapor Transmittance 
Pink — Aerosol Transmittance 



Vv- 



^M, 



_L 



T" 



T" 



1 '~ 

8 10 12 

Wavelength {\i) 



1~ 



"W.xA^^'^ 



.J^fW^^K\: 



i~ 



Figure 5. Total, H2O Continuum, H2O, and Aerosol Transmittance for 0.4 to 20 p for Advective Fog and 100 m Pathlength Utilizing Mid-Latitude Summer 
Model Atmosphere. 



Copyright © 2003 by ASME 



tioned earlier, it uses a layer-by-Iayer approach, where each layer 
parallel to the surface of the earth can be treated as a horizontal 
layer in the vicinity of the engine test stand. For the plume radi- 
ance computations, we are generally interested in a short line of 
sight within the first atmospheric layer above the ground. We 
will simplify the discussion by assuming horizontal or nearly 
horizontal line of sight. If we locate the high temperature en- 
gine plume within the same atmospheric layer, we are faced with 
the temperature incompatibility problem since by definition each 
layer consists of constant, uniform thermodynamic properties. 
This problem was resolved with the help of a NASA summer 
intern [11]. We assumed a vertical line of sight which allowed 
us to create a number of thin layers perpendicular to the line of 
sight within the plume and additional layers of larger width into 
the atmosphere. For SSME plume, for a line of sight passing 
through the Mach diamond, it can be approximated by three par- 
allel isothermal layers based on the CFD results for the plume 
[12]. For this work, we utilized recent CFD results obtained by 
J. West [13]. Essentially, the first three layers in MODTRAN 
computations model the plume. The composition of these three 
layers and other flowfield properties are based on the CFD re- 
sults. The details of the atmospheric layers and the three layers 
modeling the plume are given in Ref. [11]. Obviously, in this 
approach one has to read in all the atmospheric parameter data 
for all the layers instead of using the default values from the 
Model atmospheres. The required parameters include the alti- 
tude, the pressure, the temperature and the concentration of indi- 
vidual molecular species (total 33 species) at each layer bound- 
ary. We have considered only the radiance from the plume. The 
radiance from the engine and the test stand structural materials 
have been neglected. 

The total radiance for 0.4 to 8.0 /j for 2, 5, and 10 m path- 
lengths are shown in Fig. 6a for the SSME exhaust plume for 
1.420 X 10^ mb water vapor partial pressure in the Mach dia- 
mond. Mid-latitude summer model atmosphere has been utilized 
for concentration of other species. As expected, the total radiance 
decreases as the pathlength increases because of increased losses 
due to transmittance. Similar results for 0, 0.1, and 1.0 m path- 
lengths are shown in Fig. 6b. Here, the radiance from the most 
water vapor bands increase with increased pathlengths. This is 
because of the fact that the atmospheric layer adjacent to the 
plume is at sufficiently high temperature to contribute additional 
radiance and the transmittance losses are very small due to small 
pathlengths. The critical pathlength, the length at which the in- 
creased radiance from the 5L increase in the pathlength balances 
out the transmittance losses due to 5L, is a function of several 
variables including the temperature and pressure profiles. Fur- 
thermore, the critical pathlength is different for different bands 
of the same specie. Water vapor concentration for results shown 
above was modeled using a linear concentration profile starting 
with the CFD predicted values [13] within the three layers rep- 
resenting the SSME plume and decreasing linearly to the default 



value given by the Mid-latitude summer model atmosphere at 10 
m from the plume. At this time, there are no experimental mea- 
surements available for comparison with our results. 

We have also studied the effect of increased concentration 
of NO, N2O, and NO2 in the boundary layer and the adjacent 
atmospheric layer The radiance results have been obtained for 
the SSME plume for 2, 5, and 10 m pathlengths. Each of these 
species can affect significantly (more than 5% increase in radi- 
ance at the corresponding wavelength) if it is present at suffi- 
ciently high number density, i.e. about 1000 times the default 
value of standard atmospheric concentrations. Several different 
concentrations were tried for each specie at each pathlength. The 
radiance values for any of these species at wavelengths corre- 
sponding to their bands are complex functions of emitting band 
or line intensities, temperature of the emitting/absorbing layers 
along the line of sight, specie number density, pathlength and 
other species present. MODTRAN code does take into account 
all these factors elegantly and comprehensively. The results for 
the parametric study of plume radiance vs. nitrogen oxide con- 
centrations are not shown here for the sake of brevity. 



SUMMARY AND RECOMMENDATIONS 

We have implemented the MODTRAN code for the rocket 
engine exhaust plume radiance and transmittance computations. 
It has been shown that transmittance losses can be very, very sig- 
nificant in certain situations even for the short pathlengths. In 
general, transmittance losses can not be neglected for any path- 
length of 2 m or more. We have adapted the MODTRAN code for 
the engine plume radiance computations. If the plume composi- 
tion and flowfield parameters such as the temperature and pres- 
sure values are known along the line of sight by means of the 
experimental measurements or (more likely) CFD simulations, 
one can compute the radiance from any plume with high degree 
of accuracy at any desired point in space. 

Emission and absorption characteristics of several atmo- 
spheric and combustion species have been studied in reference 
to the rocket engine plume environments at SSC. From our point 
of view, the most important species are H2O and CO2. Other 
species which need to be included in the model are CO, N2O, 
NO2, NO, and CH4. We have also studied the effect of clouds, 
rain, and fog on the plume radiance/transmittance. The trans- 
mittance losses are severe if any of these occur along the line of 
sight. 

We have neglected the radiance emanating from the engine 
and the test stand structural materials, some of which are sure to 
be significant because of high temperatures involved. We have 
also not modeled the water vapor and other clouds which may be 
formed near the test stand during the engine firing. Obviously the 
effect of these vapor clouds can not be ignored if they are present 
along the line of sight. Currently, MODTRAN is not equipped 
to take into account these situations. Effect of plume clouds near 



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4 - 



•a 2 ■ 



I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 



,/uu 




Red-- lOmPathlength 
Green ~ 5 m Pathlength 
Blue ~ 2 m Pathlength 



..,(^- 



1 I I I I I I I I I I I I I I I I I I I I I I I I I 



I I I I I I I I I I I I I I I I I I I I I 
3 4 5 

Wavelength (fi) 



I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 



Figure 6a. Total Radiance for 0.4 to 8 /J for the SSME Plume Model for 10, 5, and 2 m Pathlength Utilizing Mid-Latitude Summer Model Atmosphere. 



I I I I I I I I. 



-a 
Pi 




Red -- 1 m Pathlength 
Green — 0.1 m Pathlength 
Blue - m Pathlength 



I 

1 



' I I I ' 

3 4 5 

Wavelength (|j) 



Figure 6b. Total Radiance for 0.4 to 8 /v for the SSME Plume Model for 1 , 0.1 , and m Pathlength Utilizing Mid-Latitude Summer Model Atmosphere. 



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the engine test stands needs to be modeled and studied for a better 
understanding of engine plume radiance/transmittance. 



ACKNOWLEDGEMENTS 

The author would like to thank S. Leung for carrying out 
very diligently hundreds of spectral simulations required for the 
parametric studies. L. Langford provided his superb expertise 
with computers during many phases of this work. CFD results 
were provided by J. West (now at MSFC). The author would also 
like to thank Dr West for many stimulating discussions. The 
author would like to thank W. St. Cyr, R. Daines, and D. Paul 
Taliancich for reviewing the manuscript and making many useful 
suggestions. R. Menge did an excellent job in typing this report. 
Her dedication and patience is appreciated. 



REFERENCES 

[1] Kneizys, F. X., Shettle, E. R, Abreu, L. W., 
Chetwynd, J. H., Anderson, G. R, Gallery, W. O., Selby, J. E. 
A., and Clough, S. A., Users Guide to LOWTRAN 7, AFGL-TR- 
88-0177, Air Force Geophysics Laboratory, Hanscom AFB, MA. 
August 16, 1988 

[2] Rothman, L. S., Rinsland, C. R, Goldman, A., 
Massie, S. T., Edwards, D. R, Flaud, J.-M ., Perrin, A., Camy- 
Peyret, C, Dana, V., Mandin, J.-Y., Schroeder, J., McCann, A., 
Gamache, R. R., Wattson, R. B., Yoshino, K., Chance, K. V., 
Jucks, K. W., Brown, L. R., Nemtchinov, V., and Varanasi, P., 
''The HITRAN Molecular Spectroscopic Database and Hawks 
(HITRAN Atmospheric Workstation): 1996 Edition,'' Journal of 
Quantitative Spectroscopy and Radiative Transfer 60 (5), 665, 
1998. 

[3] Acharya, P. K., Berk, A., Bernstein, L. S., Matthew, 
M. W., Adler-Golden, S. M., Robertson, D. C, Anderson, G. P, 
Chetwynd, J. H., Kneizys, F X., Shettle, E. P, Abreu, L. W., 
Gallery, W. O., Selby, J. E. A., and Clough, S. A., MODTRAN 
User's Manual, Version 3. 7 and 4.0, Air Force Research Labora- 
tory, Hanscom AFB, MA, December 1, 1998. 

[4] Penner, S. S., Quantitative Molecular Spectroscopy 
and Gas Emissivities, Addison-Wesley, Reading, MA, 1959. 

[5] Goody, R. M., Atmospheric Radiation, Theoretical 
Basis, Oxford University Press, Oxford, Great Britain, 1961. 
See also. Goody, R. M., and Yung, Y L., Atmospheric Radia- 
tion, Theoretical Basis, Second Edition, Oxford University Press, 
New York, NY, 1989. 

[6] See, for example, Selby, J. E. A., and McClatchey, 
R. A., Atmospheric Transmittance from 0.25 to 28.5 /jm: Com- 
puter Code LOWTRAN 3, Air Force Cambridge Research Lab- 
oratories, Hanscom AFB, MA, May 7, 1975; Kneizys, F X., 
Shettle, E. P,. Gallery, W. O., Chetwynd, Jr, J. H., Abreu, 
L. W., Selby, J. E. A., Clough, S. A., and Fenn, R. W., Atmo- 
spheric Transmittance/Radiance: Computer Code LOWTRAN 6, 



Air Force Geophysics Laboratory, Hanscom AFB, MA, August 
1, 1983. 

[7] See, for example, Tejwani, G. D., ''Improved Calcu- 
lated Linewidths for H2O Broadened by N2," Journal of Quanti- 
tative Spectroscopy and Radiative Transfer 40 (5), 605 (1988). 

[8] Tejwani, G. D., and Varanasi, P., 'Approximate 
Mean Absorption Coefficients in the Spectrum of Water Vapor 
Between 10 and 22 Microns at Elevated Temperatures," Jour- 
nal of Quantitative Spectroscopy and Radiative Transfer 10, 373 
(1970). 

[9] Herzberg, G., Molecular Spectra and Molecu- 
lar Structure II. Infrared and Raman Spectra of Polyatomic 
Molecules, D. Van Nostrand Company, Princeton, NJ (1945). 

[10] Tejwani, G.D., "Transmittance and Radiance 
Computations for the SSC Engine Plume Environments," Lock- 
heed Martin Stennis Operations, SSC, MS, October 31, 2002. 

[11] Leung, S., "Parametric Study of the Plume Ra- 
diance and Atmospheric Transmission Attenuation in Stennis 
Space Center Environment," National Aeronautics and Space 
Administration, SSC, MS, August 2, 2002. 

[12] Tejwani, G. D., and Thurman, C. C, "Rocket 
Engine Plume Spectral Simulation and Quantitative Analysis," 
NASA CP 3282, Vol. I, Advanced Earth-to-Orbit Propulsion 
Technology, Huntsville, AL, May 17-19, 1994. 

[13] West, J., "Plume Properties for Large Throat 
SSME on the B-1 Test Stand," Lockheed Martin Stennis Oper- 
ations, SSC, MS, January 27, 1998 (UnpubHshed Notes). 



10 



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Transmittance and radiance Computations for Rocket Engine Plume 
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Gopal Tejwani 



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14. ABSTRACT 

Rocket engine exhaust plume is generally thermal in character arising from changes in the internal energy of constituent molecules. 
Radiation from the plume is attenuated in its passage through the atmosphere. In the visible and the infrared region of the spectrum fo: 
clear-sky conditions, this is caused mainly through absorption by atmospheric molecular species. The most important 
combustion-product molecules giving rise to emission in the IR are water v^or, carbon dioxide, and carbon monoxide. In addition, 
the high temperature plume reacting with the surrounding atmosphere may produce nitrogen oxides, in the boundary layer, all of 
which are strongly emitting molecules. Important absorbing species in the atmosphere in the engine plume environment are H20, CO. 
C02, CH4, N20,N0, andN02. Under normal atmospheric conditions, the concentrations of 03, S02, andNH3 are too small to 
produce any significant absorption. Essentially the problem comprises of the propagation of radiation from a hot gas source through a 
long cool absorbing atmospherethus combining aspects of atmospheric and combustion gas methods. Since many of the same 
molecular species are responsible for both emission and absorption, the high degree of line position correlation between the emission 



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